Mathematical and statistical modeling techniques are relevant to biomedical investigations at a variety of scales and in a variety of contexts. Our Lab applies expertise in the mathematical, statistical and computing sciences to address novel problems arising in cutting edge areas of biomedical research. In a joint study with investigators in Laboratory of Molecular Biology, NCI and Institut National de la Recherche Agronomique (INRA), France, we are attacking the problem of protein structure classification, with the goal of improving automated methods for recognition and classification of protein domains in three dimensional structures. Domains are thought to be the building blocks of complex structures, and often determine protein function. Our current project compares two existing protein structure similarity detection methods (VAST and SHEBA) and contrasts them with a manually curated protein classification, SCOP. A large representative database of structures has been used to identify ambiguous classes of proteins which neither automated method effectively distinguishes. Automated hierarchical clustering based on VAST and SHEBA similarity scores has been tested and compared to the SCOP classification. A manuscript describing our results is under review. With an investigator in the Laboratory of Receptor Biology and Gene Expression, National Cancer Institute, and with another investigator from Imperial College, London, who was a visitor to NCI, we have studying the physical topology of gene and chromosome placement in cell nuclei. This work requires careful statistical analysis on data collected of gene and chromosome placement data. We have shown that in mice, the gene MASH1, involved in early embryonic neurogenesis, is preferentially placed in the nuclear periphery in embryonic stem cells, but migrates towards the nuclear center after commitment to neural development. It was shown, too, that the physical change in location was coupled to changes in expression level and to changes in chromatin structure along a 2MB region of the genome centered about the MASH1 locus. A manuscript describing this is under referee review. With an investigator in the Division of International Epidemiology, Fogarty International Center, we have developed a phenomenological model of Plasmodium parasite/red blood cell dynamics, and have used it to examine the consequences of strategies of attack of the different Plasmodium species that attack humans. Currently, we are investigating consequences of dual P. vivax- P. falciparum infection. (PCR studies indicate that about 10% of all human malaria cases are dual P. vivax-P. falciparum infections.) Our studies indicate transients in red blood cell production induced in response to P. falciparum invasion of such cells can greatly boost the parasitemia of P. vivax, even inducing a cryptic infection into a more dangerous phase. A manuscript describing this work is under review. Investigators in NICHD and CIT have created Extended Microcapture Dissection (or XMD), a major revision of the laser capture microdissection (LCM) device that was developed here at NIH in the mid 1990?s. In this new form of microtransfer using thermoplastic films, the intrinsic absorption of stained tissue heats up the polymer and causes it to melt and form a thermoplastic bond similar to that in LCM. We have performed thermal diffusion modeling to assist in optimizing the design or operations of this new device. Prototypes have been built and the focus is currently on the testing of prototypes. In a continuing project with investigators in the Laboratory of Integrative and Medical Biophysics, NICHD related to the development of diffusion tensor MRI on using Non-Uniform Rational B-Splines (NURBS) for extracting geometrical features of the basic brain anatomy, with ultimate goal of developing a continuous tensor model based on NURBS, we showed how some important differential geometric quantities can be determined more reliably than with other models. This is published in a book chapter. In another project with the same group we propose a novel method for performing true spectral decomposition of the tensor valued random variables, rather than performing it using rasterized (vectorized) tensors. In a project, with investigators of NIMH, we analyzed multiple-electrode recordings from in-vitro neural network preparations in order to deduce the underlying cortical networks topology. We obtained the results for the organotypic rat brain preparations, which show a strong "small world" property, meaning high clustering among the nodes and short node-to-node distances. We conducted large scale simulations to verify those results. The ultimate goal is to understand the relationship between the topology of the network and the functions that it performs.